Model of Temperature Dependence Shape of Ytterbium-doped Fiber Amplifier Operating at 915 nm Pumping Configuration

We numerically analyze the temperature dependence of an ytterbium-doped fiber amplifier (YDFA) operating at 915 nm, investigating its gain and Noise Figure properties variation with temperature. The temperature-dependent gain and noise figure variation with YDFA length are numerically obtained for the temperature range of +20 0 C to +70 0 C. The results show that good intrinsic output stability against temperature change can be achieved in ytterbium doped fiber amplifiers even when operating at high gain regime with small signal input. This result demonstrates the great potential for stable high power laser communication systems based on ytterbium system.


I. INTRODUCTION
Fiber lasers and amplifiers have attracted great interest recently, because they offer the advantages of compact size, high gain, guided mode propagation, better stability and their outstanding thermo-optical properties [1][2][3][4].Ytterbium (Yb 3+ )doped fiber Amplifier (YDFA) has a great potential because it does not have some of the drawbacks associated with erbiumdoped amplifier: excited state absorption phenomenon that can reduce the pump efficiency and concentration quenching by interionic energy transfer do not occur, and high doping levels are possible.Thus, it offers high output power (or gain) with a smaller fiber length.YDFA's have a simple energy level structure and provide amplification over a broad wavelength range from 975 to 1200 nm.Moreover, YDFA's can offer high output power and excellent power conversion efficiency [1,[5][6][7][8][9][10][11][12].
This paper explores the effects of temperature on amplifier performance.For an amplifier, the temperature affects relative extraction by the signal and ASE.Thermal management is a critical issue and cannot be ignored.Some papers about temperature effect of Er 3+ -doped fiber laser and amplifier were reported [15][16][17].Temperature can affect the absorption and emission cross sections [2].This paper demonstrates output characteristics of Yb 3+ -doped fiber laser at different temperatures degrees.So from this research the temperature can affect the gain and noise figure (NF) at different length.
Established methods of modeling erbium amplifiers can be used to model ytterbium system [11,[18][19].However, modeling temperature sensitivity is completely different.The small energy gaps in the relevant stark levels in erbium systems, makes the determination of distinct sub-transition characteristics quite difficult [17], while this is not true in ytterbium system.Accurate characterization of Yb 3+ absorption and emission cross sections is crucial [20,21].

II. THEORETICAL MODEL
We used standard rate equations for two-level systems to describe the gain and propagation characteristics of the Ybdoped fiber amplifier operating at 975 nm because the ASE power is negligible for a high power amplifier with sufficient input signal (about 1 mW).After the overlap factors are introduced and the fiber loss ignored, the simplified two-level rate equations and propagation equations are given as follows [12]: Here, N 0 is the Yb-dopant concentration, N 1 and N 2 are the ground and upper-level populations.s  and p  are the oveperlapping factor between the pump (signal) and the fiberdoped area.
A. Spectroscopy of ytterbium in silica Ytterbium in silica is a simple, two level system having four Stark levels in the lower manifold F 7/2 and three Stark levels in upper manifold F 5/2 .An energy level diagram specific to Nufern 5/125 fiber is shown in Figure 1 [22].Because the splitting of the levels depends on the glass composition, concentration of dopants and co-dopants, and the degree of structure disorder of the glass network, the energy level diagram for Yb in silica may vary with each individual fiber.The absorption and emission cross-sections for Yb in silica are related to the temperature and the energy of the levels by the following relationships: where E x are the energies of the level difference between level x and a, when x (a,d) where a is the ground state in lower manifold and the energies of the level difference between levels x and e, in the ground state in upper manifold when x (e,g), T is the temperature, K= Where N 1 and N 2 are Yb doping concentration at the upper and lower energy levels, respectively.Using the absorption and emission cross section from Eqs. (7)(8)(9)(10)(11), and the propagation equations ( 3) and ( 4) can even be solved analytically in this case [23].
The small signal gain G for active length of the fiber L can be given by   21 ( ) exp ( ( , ) ( , ) ) Figure 2 and 3 show the variation of Yb absorption and emission cross sections at various temperatures respectively [21].It is clear from figure 3 that the signal absorption cross section declines with increasing wavelength and it is almost 0 at 1064 nm.The term 1 ( , ) sa N z t  can be ignored as it is a decreasing function of signal wavelength, then   Where G is the gain and amp P is the spectral density of ASE generated by the doped fiber.For input ASE gives the signal spontaneous beat noise (1/G) limited noise figure as a function of the signal gain and input and output ASE spectral densities therefore the NF can be expressed as: Where 1/G is the beat noise, ()  is the output ASE spectral density (Watt/Hertz) at signal wavelength, ()  is the input ASE spectral density at signal wavelength, and s  is the frequency of the signal wavelength.For lower gains, a much simpler model which ignores the effect of ASE on the level populations can be used, so the ( ) For each signal wavelength the noise figure can be calculated in decibel (dB) and is given by: www.ijacsa.thesai.org

III. RESULTS AND DISSCUSSIONS
For numerical calculation, the fiber parameters for YDFA amplifier are shown in Table 1.We studied the variation of gain and NF with the length of the amplifier over the temperature range from 20 o C to 70 o C at signal wavelength of 1064 nm.The results are shown in Figures 4 and 5, respectively.It is clear from the results that the signal gain raises with increases in the length, at the same time the gain declines when the temperature increases.However the NF increases when the temperature rises.Furthermore the NF increases with increasing the length.It is clear from the results that the variation of the NF with temperature is minimal for lengths over 5 m.

IV. CONCLUSION
A YDFA model has been introduced including the temperature effects for gain and noise figure of a length of the YDFA amplifier.The temperature dependence of the gain and noise figure on various temperatures was taken into consideration which shows that the performance of YDFA exhibit excellent low temperature sensitivity.The analytical solution of the propagation equations has also been derived for the temperature range from 20 0 C, to +70 0 C for finding the gain.These results demonstrate that highly stable ytterbium doped fiber amplifiers can potentially be achieved.
Table 1: The fiber parameters symbols used in the numerical calculations [18] Value Definitions Symbol
emission (ASE) noise spectrum uses the noise figure (NF) given or as input parameter.In the practical case the ASE is presented at input of the doped fiber, therefore the amplified input ASE i ASE P spectral density can be added to the amplified output ASE spectral density

Figure 4 :
Figure 4: The change of the signal gain with temperature and length.

Figure 5 :
Figure 5: The change of the Noise Figure with temperature and length.
signal and pump light, respectively.A is the doped area of the fiber. is the upper state lifetime.
( , ),( , )sp P z t P z t are the signal and pump power respectively.sa se and  are the signal absorption and emission cross sections.and sp  are the www.ijacsa.thesai.orgfrequencies of